Stratified Random Sampling

Stratified Random Sampling, also sometimes called proportional or quota random sampling, involves dividing your population into homogeneous subgroups and then taking a simple random sample in each subgroup. In more formal terms:

Objective: Divide the population into non-overlapping groups (i.e., strata)
N₁, N₂, N₃, ... N_i,
such that N₁ + N₂ + N₃ + ... + N_i = N.
Then do a simple random sample of
f = n/N in each strata.

There are several major reasons why you might prefer stratified sampling over simple random sampling. First, it assures that you will be able to represent not only the overall population, but also key subgroups of the population, especially small minority groups.If the subgroup is extremely small, you can use different
sampling fractions (f) within the different strata to randomly over-sample the small group although you'll then have to weight the within-group estimates using the sampling fraction whenever you want overall population estimates). When we use the same sampling raction within strata we are conducting proportionate stratified random sampling.
When we use different sampling fractions in the strata, we call this disproportionate stratified random sampling. Second, stratified random sampling will generally have more statistical precision than simple random sampling. This will only be true if the strata or groups are homogeneous. If they are, we expect that the variability within-groups is lower than the variability for the population as a whole. Stratified sampling capitalizes on that fact.